Decay of the Mediator Particle at Threshold

A light mediator particle is often predicted in the dark sector scenario, which weakly interacts with the standard model (SM) particles. The weakness of the interaction is usually described by a small coupling; however, the small coupling does not always guarantee the weakness of the interaction. When the mass of the mediator particle lies in a threshold region, the so-called threshold singularity may emerge, and then the perturbative calculation fails. This singularity causes several effects, e.g., the mixing between the mediator particle and bound states, the Sommerfeld effect on the final state of the mediator particle decay, etc. Taking the minimal model of the vector mediator particle decaying mainly into the SM particles as an example, we develop a method to describe the singularity quantitatively. We also calculate some physical quantities using this method, such as the lifetime of the mediator particle, and find that those could be significantly altered compared with the result of the perturbative calculation.